STOR 435
Handout 12
Sections 6.1
Example 1
(Exercise 6.1.a, Joint dist, Discrete)
.
Two fair dice are rolled.
Find the joint probability mass function of
X
and
Y
when
X
is the largest
value obtained on any die and
Y
is the sum of the values
Example 2
(Exercise 6.6, Joint dist, Discrete )
.
A bin of 5 transistors is known
to contain 2 that are defective. The transistors are to be tested, one at a time,
until the defective ones are identi±ed. Denote by
N
1
the number of tests made
until the ±rst defective is identi±ed and by
N
2
the number of additional tests
until the second defective is identi±ed. Find the joint probability mass function
of
N
1
and
N
2
. Now ±nd the probability mass function of just
N
1
.
Example 3
(Joint dist; continuous)
.
The joint density of
X
and
Y
is given by
f
(
x,y
) =
b
2
e

x
e

2
y
0
< x <
∞
,
0
< y <
∞
0
otherwise
Compute
1.
P
(
X >
1
,Y <
1),
2.
P
(
X < Y
)
3.
P
(
X < a
)
Example 4
(Example 1d; Joint dist; continuous)
.
Consider a circle of radius
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 Spring '11
 Shakar
 Probability theory, probability density function, Probability mass function, Joint Dist

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